I am designing a temperature sensor using an interdigitated capacitor. Using the electrostatics modules, I was successfully able to design the sensor with the starting capacitance value I wanted. However, regarding changing capacitance with temperature is where I run into problems. Thus far, I have been using the joule heating and thermal expansion module. Can anyone tell me if this is the correct module for my goal?

I have had some measure of success using it. However I find that when I remove the surrounding rectangle with air associated with it in the positive z direction and silicon in the negative z direction, the study completes, but with that rectangle, I get an error of singular matrix/solution does not converge and cannot complete the study. Why is this?

Also, without the surrounding rectangle, and without the proper dielectric in place, it seems that I cannot calculate capacitance correctly, and the values are all very small, approaching zero.

it seems that your model has not uploaded correctely (it has a size of 0 bytes, not very instructive). You probably need to make it smaller by clearing the results first: Edit Clear all results + Edit Clear All Mesh + File Reset Model + Save"

I suspect, from what you say that you have an issue with the materials and the different physics. You need the "air" for the ACDC simulation but not for the structural, as air has not defined in the Young modulus and poisson coefficient etc

You need to study a little the examples in the model library that looks close to yours, either by splitting up the simulation, or by giving the air a "pseudo linear material property, such as poisson = 0 and a low E modulus 1/3 of the ambient pressure for example. Or you need te FSI moule, perhaps an overkill for your case

I did get both the ES and TEM modules to simulate when the air material and the domain associated with it (domain 2) are disabled.

There is still one thing I have not yet been able to figure out however, when I specify to calculate the capacitance from solution 2(the electrostatics study), I get a capacitance value in the range I want, 0.0048pF. However, if I specify the capacitance to be calculated from solution 1 (the joule heating and thermal expansion study), I cannot make sense of the value calculated, just got -2.9e-26?

This is problematic as my ultimate goal is to calculate the capacitance with changing temperature. Can I accomplish this with my current model? I have not yet found another example model that appears to do what I want to use for guidance.

but how can you get a capacitive value from two structures if you do not define the air around ? you cannot solve the field since there is no domain to solve the ES field in ? Or have I misunderstood you ?

Also I do not understand how you can get any Joule heating, where is your current flowing ? in the Si substrate ?

I suppose I do not understand your model there, I believe you must explain a bit more for us out here to catch it better ;)

Getting a change in dimensions by Joule heating for MEMS is rather standard, and as the cpacity is calculated from the geometry and the dielectric constant of the surrounding medium (air ususally, or vacuum) it will change with the thermal expansion, and for that a separate ES analysis in 3D to get all fringe effects is useful and is a "standard methode" I would say

Background info: I am designing a MEMS capacitive temperature sensor. I am applying a voltage to the lower comb and grounding the upper comb in the model. The lower comb is also movable while the upper comb, substrate, and anchors on the model are fixed in place. I am using the TEM physics to get a displacement of the movable comb with temperature and seem to have accomplished this. I then would like to calculate the capacitance of the resulting deformed structure using the ES physics. I have not yet figured out how to do this however.

When you speak of separating the models, do you mean create a model 1 and a model 2 in the same file and specify TEM for model 1 and ES for model 2? This is how I took what you said to mean and attempted to do this in the attached file.

If you look at it, I specified the geometry in model 1 and applied the TEM physics to get a displacement of the movable comb with temperature. In model 2, I specified the ES physics and to import the deformed geometry from study 1 into this model. I also added the air layer to this model since I want to use the ES physics to calculate capacitance from the deformed geometry. However when I attempt to mesh model 2, I receive a "matrix is zero" error. I looked at the knowledge base article on the matter, which says to check that the mesh extends to the volume and this appears to be the case when I check the settings window of the mesh as it specifies. Any other suggestions on this "matrix is zero" error when meshing?

Well I find it's not that easy to understand your model. You apply joule heating via TEM, but there is no current flowing in your capacitive actuator and your Si substrate is of high impedance, first question: what is imposing the temperature rise ?
And for ES you apply the voltage to all external boundaries as you have no current flow that I understand, while for Joule heating you normally apply the voltage to the wire bounding entries (1-2 BCs) and leave the current flow naturally through the system.

With two models it's not easy to couple the deformations from one to the next one, specially when you change the topology between both (add in the air) I would rather use 1 model, but 2 physics and solve them in sequence once per physics, and add in the air for both but that is not a big issue.

Trick for your meshing: cut the air with layers at the different step heights (underneath and above your blade heights) then you can use a swep mesh and get 3-5 nodes per height element, your results will be more precise. You might consider boundary elements to better catch the voltage changes along the actuator boundary normals